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z-z-2-3x-3y-0-show-that-2-z-x-2-2-z-y-2-2z-x-1-z-2-x-3-




Question Number 89236 by 675480065 last updated on 16/Apr/20
z(z^2 +3x)+3y=0  show that  (∂^2 z/∂x^2 )+(∂^2 z/∂y^2 )=((2z(x−1))/((z^2 +x)^3 ))
$$\mathrm{z}\left(\mathrm{z}^{\mathrm{2}} +\mathrm{3x}\right)+\mathrm{3y}=\mathrm{0} \\ $$$$\mathrm{show}\:\mathrm{that} \\ $$$$\frac{\partial^{\mathrm{2}} \mathrm{z}}{\partial\mathrm{x}^{\mathrm{2}} }+\frac{\partial^{\mathrm{2}} \mathrm{z}}{\partial\mathrm{y}^{\mathrm{2}} }=\frac{\mathrm{2z}\left(\mathrm{x}−\mathrm{1}\right)}{\left(\mathrm{z}^{\mathrm{2}} +\mathrm{x}\right)^{\mathrm{3}} } \\ $$
Answered by niroj last updated on 16/Apr/20

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